Bulletin

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Volume 37 • Number 2 • 2014

• Mean Residual Life of kth Records Under Double Monitoring
O.M. Bdair and M.Z. Raqab

Abstract.
In the study of reliability of technical systems and shock models, the mean \linebreak residual life function plays an important role. In this paper, we consider the mean residual life of

$k$ th records under double monitoring. We introduce the notion of the mean residual life of

$k$ th records under the condition that the

$m$ th and

$(m+1)$ st shocks arrived before and after

$t_1$ , respectively, and the

$(n+1)$ st

$(1 ≥ m < n)$ shock arrived after

$t_{2}$

$(0 < t_{1} < t_{2})$ . We study their respective monotonicity and aging properties. Some stochastic ordering \linebreak properties are also investigated.

2010 Mathematics Subject Classification: 62E10, 60E05

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